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Algebra Seminar
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Ruibin Zhang
University of Sydney

Kazhdan-Lusztig polynomials for Lie superalgebras and a duality theorem

Friday 17th September, 12:05-12:55pm, Carslaw 175.

An isomorphism is established between Grothendieck groups of the type A Lie algebra and Lie superalgebra in the inductive limit. The proof is derived from the respective Kazhdan-Lusztig theories for the algebras reformulated in terms of canonical bases of a quantum group. A consequence of this isomorphism is that the usual parabolic Kazhdan-Lusztig polynomials of type A compute the characters of the finite dimensional irreducible representations of the general linear superalgebra. This is joint work with Cheng (Taiwan) and Wang (Virginia).